Improved stochastic process models for linear structure behavior

Paez, Thomas L.; Lacy, Seth L.; Babuška, Vít; Miller, Daniel N.

doi:10.1109/acc.2011.5991434

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…As noted in Ref. 8, some of these FRFs represent physically unlikely systems. For example, some of the FRFs contain positive peaks where they should be negative and some have more than 6 peaks.…”

Section: B Kle Based Frf Generationmentioning

confidence: 98%

“…This step is omitted, but can be seen in Ref. 8. Using test data denoted by , * + where is the number of test realizations, the components of the KLE in Eq.…”

Section: Expanding a Test Ensemblementioning

confidence: 99%

“…Starting with a small ensemble of test data, a large synthetic ensemble is created by using a Karhunen-Loeve decomposition combined with a Kernel Density Estimator and a Metropolis-Hastings Markov Chain Monte Carlo randomization as described in Ref. 8. This expanded set of test data is then evaluated using stability and performance metrics described in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Data-Based Stochastic Evaluation of Closed-Loop Stability and Performance

Krattiger¹,

Lacy²,

Lane³

et al. 2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite

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Metrics for determining the stability-and performance-robustness of a given controller to variations in open-loop dynamics are examined. Of particular interest are the probability distributions that these metrics have given some amount of uncertainty in the plant. The analysis herein characterizes these distributions using frequency response data collected experimentally for the open-loop plant. In doing so, it avoids using a model for the plant, thereby reducing errors and uncertainty inherent to the modeling of a plant. For a proposed controller, a Monte-Carlo method is used to evaluate the closed-loop performance and stability metrics for a large ensemble of test data and thus create an estimate of their distributions. Since ensembles of test data are typically quite small, a Karhunen-Loeve expansion based method is used to synthetically expand the set of FRFs. Nomenclature = Random process vector = Mean vector for random process = j th experimental realization of random process vector = Orthogonal basis vectors = Weighting matrix = Linear combination vector = Deviation matrix ( ) = Estimated from experimental data = Length of random process vector = Number of contributing basis vectors = Number of experimental realizations = Smoothing parameter = Kernel density estimator = Perturbation of linear combination vector 2 = Candidate combination vector ̃ = l th Metropolis-Hastings Monte-Carlo generated combination vector for j th test realization = Probability of acceptance for candidate combination vector = Acceptance parameter ( ) ( ) = Generated using Metropolis-Hastings Monte Carlo = Performance and stability cost function = Closed-loop, open-loop, and controller transfer functions = k th frequency point in transfer function = Number of outputs in transfer function = Number of inputs in transfer function = Physical Mass, Stiffness and Damping Matrices = Modal damping matrix = Modal damping parameter for r th mode = r th natural frequency = Mode Matrix = State-space matrices = Cholesky decomposition of mass matrix = Random matrix of zero mean, independent, normally distributed variables = Dispersion level = Number of degrees of freedom in model = Second dimension of random matrix

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Section: B Kle Based Frf Generationmentioning
confidence: 98%

“…This step is omitted, but can be seen in Ref. 8. Using test data denoted by , * + where is the number of test realizations, the components of the KLE in Eq.…”

Section: Expanding a Test Ensemblementioning
confidence: 99%

Section: Introductionmentioning
confidence: 99%

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Data-Based Stochastic Evaluation of Closed-Loop Stability and Performance
Krattiger¹,
Lacy²,
Lane³
et al. 2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite
0
0
0
0
View full text Add to dashboard Cite
Metrics for determining the stability-and performance-robustness of a given controller to variations in open-loop dynamics are examined. Of particular interest are the probability distributions that these metrics have given some amount of uncertainty in the plant. The analysis herein characterizes these distributions using frequency response data collected experimentally for the open-loop plant. In doing so, it avoids using a model for the plant, thereby reducing errors and uncertainty inherent to the modeling of a plant. For a proposed controller, a Monte-Carlo method is used to evaluate the closed-loop performance and stability metrics for a large ensemble of test data and thus create an estimate of their distributions. Since ensembles of test data are typically quite small, a Karhunen-Loeve expansion based method is used to synthetically expand the set of FRFs. Nomenclature = Random process vector = Mean vector for random process = j th experimental realization of random process vector = Orthogonal basis vectors = Weighting matrix = Linear combination vector = Deviation matrix ( ) = Estimated from experimental data = Length of random process vector = Number of contributing basis vectors = Number of experimental realizations = Smoothing parameter = Kernel density estimator = Perturbation of linear combination vector 2 = Candidate combination vector ̃ = l th Metropolis-Hastings Monte-Carlo generated combination vector for j th test realization = Probability of acceptance for candidate combination vector = Acceptance parameter ( ) ( ) = Generated using Metropolis-Hastings Monte Carlo = Performance and stability cost function = Closed-loop, open-loop, and controller transfer functions = k th frequency point in transfer function = Number of outputs in transfer function = Number of inputs in transfer function = Physical Mass, Stiffness and Damping Matrices = Modal damping matrix = Modal damping parameter for r th mode = r th natural frequency = Mode Matrix = State-space matrices = Cholesky decomposition of mass matrix = Random matrix of zero mean, independent, normally distributed variables = Dispersion level = Number of degrees of freedom in model = Second dimension of random matrix
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Modeling and Simulation of Parameter Vector Random Processes in Mechanical Structures
Babuška¹,
Lacy²,
Lane³
et al. 2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
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Improved stochastic process models for linear structure behavior

Cited by 2 publications

References 12 publications

Data-Based Stochastic Evaluation of Closed-Loop Stability and Performance

Data-Based Stochastic Evaluation of Closed-Loop Stability and Performance

Modeling and Simulation of Parameter Vector Random Processes in Mechanical Structures

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